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TMF, 2010, Volume 164, Number 2, Pages 214–221 (Mi tmf6535)  

This article is cited in 13 scientific papers (total in 13 papers)

The Korteweg–de Vries equation with a self-consistent source in the class of periodic functions

A. B. Khasanov, A. B. Yakhshimuratov

Urgench State University, Urgench, Uzbekistan

Abstract: We use the inverse spectral problem method to integrate the Korteweg–de Vries equation with a self-consistent source in the class of periodic functions.

Keywords: Sturm–Liouville operator, spectral data, system of Dubrovin equations, Korteweg–de Vries equation with a self-consistent source

DOI: https://doi.org/10.4213/tmf6535

Full text: PDF file (366 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2010, 164:2, 1008–1015

Bibliographic databases:

Received: 13.02.2009
Revised: 06.01.2010

Citation: A. B. Khasanov, A. B. Yakhshimuratov, “The Korteweg–de Vries equation with a self-consistent source in the class of periodic functions”, TMF, 164:2 (2010), 214–221; Theoret. and Math. Phys., 164:2 (2010), 1008–1015

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Yakhshimuratov, “Integrirovanie uravneniya Kortevega-de Friza so spetsialnym svobodnym chlenom v klasse periodicheskikh funktsii”, Ufimsk. matem. zhurn., 3:4 (2011), 144–150  mathnet  zmath
    2. Yakhshimuratov A., “The Nonlinear Schrodinger Equation with a Self-consistent Source in the Class of Periodic Functions”, Math Phys Anal Geom, 14:2 (2011), 153–169  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. M. M. Matyoqubov, A. B. Yakhshimuratov, “Integration of higher Korteweg-de Vries equation with a self-consistent source in class of periodic functions”, Ufa Math. J., 5:1 (2013), 102–111  mathnet  crossref  mathscinet  elib
    4. A. Cabada, A. Yakhshimuratov, “The System of Kaup Equations with a Self-Consistent Source in the Class of Periodic Functions”, Zhurn. matem. fiz., anal., geom., 9:3 (2013), 287–303  mathnet  mathscinet
    5. Yakhshimuratov A.B., Khasanov M.M., “Integration of the Modified Korteweg-de Vries Equation With a Self-Consistent Source in the Class of Periodic Functions”, Differ. Equ., 50:4 (2014), 533–540  crossref  mathscinet  zmath  isi  scopus
    6. Babajanov B., Feckan M., Urazboev G., “On the Periodic Toda Lattice With a Self-Consistent Source”, Commun. Nonlinear Sci. Numer. Simul., 22:1-3 (2015), 1223–1234  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. B. A. Babajanov, A. B. Khasanov, “Periodic Toda chain with an integral source”, Theoret. and Math. Phys., 184:2 (2015), 1114–1128  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. A. B. Yakhshimuratov, M. M. Matyokubov, “Integration of loaded Korteweg–de Vries equation in a class of periodic functions”, Russian Math. (Iz. VUZ), 60:2 (2016), 72–76  mathnet  crossref  isi
    9. Shen Ya., Yao R., “Solutions and Painleve Property For the Kdv Equation With Self-Consistent Source”, Math. Probl. Eng., 2018, 4014382  crossref  mathscinet  isi  scopus
    10. A. B. Hasanov, M. M. Hasanov, “Integration of the nonlinear Schrödinger equation with an additional term in the class of periodic functions”, Theoret. and Math. Phys., 199:1 (2019), 525–532  mathnet  crossref  crossref  adsnasa  isi  elib
    11. A. B. Yakhshimuratov, “Integration of a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions”, Theoret. and Math. Phys., 202:2 (2020), 137–149  mathnet  crossref  crossref  isi  elib
    12. Ufa Math. J., 12:1 (2020), 103–113  mathnet  crossref  isi
    13. A. B. Khasanov, M. M. Matjakubov, “Integration of the nonlinear Korteweg–de Vries equation with an additional term”, Theoret. and Math. Phys., 203:2 (2020), 596–607  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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